The Set of Circular Flow Numbers of Regular Graphs

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Abstract

This article determines the set of the circular flow numbers of regular graphs. Let math formula be the set of the circular flow numbers of graphs, and math formula be the set of the circular flow numbers of d-regular graphs. If d is even, then math formula. For math formula math formula it is known [6] that math formula. We show that math formula. Hence, the interval math formula is the only gap for circular flow numbers of math formula-regular graphs between math formula and 5. Furthermore, if Tutte's 5-flow conjecture is false, then it follows, that gaps for circular flow numbers of graphs in the interval [5, 6] are due for all graphs not just for regular graphs.

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